Republican presidential candidate Mitt Romney barnstormed Ohio on Wednesday amid signs that the battleground state – and perhaps other key battlegrounds as well – is slipping farther from his grasp.

With President Barack Obama also campaigning in the state, Romney sharpened his economic and deficit message on a daylong bus tour through the rainy Buckeye State, an unusually busy day for a candidate who hasn’t done a lot of multiple campaign events on the road lately.

The stepped-up campaigning came six weeks before Election Day as a series of new polls shows Romney falling behind Obama in several swing states – including Ohio, Florida and Virginia – as well as on major issues.

He now trails by an average of 5.2 percentage points in Ohio, 4.5 points in Virginia, 4.2 points in Nevada, 4 points in Iowa and 3.1 points in Florida, according to data compiled by the nonpartisan website RealClearPolitics.com.

He trails the president or is at best neck and neck on most economic issues in the eyes of likely voters in Ohio and Florida, according to a new poll for The Washington Post.

Romney on Wednesday was looking to boost his standing as he heads toward a potentially make-or-break showdown with Obama in the first of three debates next Wednesday.

Speaking at a rally in a high school gym in Westerville, Romney assailed the president for his stewardship of the troubled economy.

“Do we really want four more years where half the kids coming out of college can’t find work, college-level work?” Romney asked the more than 1,000 supporters in the audience.

“No!” they responded.

“I don’t think we can afford four more years like the last four years.”

Ohio is crucial for Romney. No Republican has won the presidency without winning Ohio, and given the leanings of other states, there’s no visible electoral map strategy that the former Massachusetts governor can craft to win the White House without Ohio, analysts said.

“The math just doesn’t support it, and the Obama people know that if he (Obama) wins Ohio, it’s game over,” said David Cohen, a political science professor at the University of Akron.

Obama carried the state by 5 percentage points in 2008. But Republicans have made significant inroads in Ohio since then – taking back the governor’s mansion and winning more seats in Congress – giving them hope that the state would stay in the Republican column for Romney.

In Westerville, Jim and Rhonda Britt proudly wore Romney-for-president buttons and carried Romney signs. They struggled to understand why he seemed to be losing ground to the president in Ohio polls.

“I don’t think the polling is correct,” said Jim Britt, 55, who owns a Columbus delivery service. “I see more energy from Romney than I did from John McCain” when he ran for president in 2008.

“After all the debates, after the campaigns, after all the ads are over, the people of Ohio are going to say loud and clear on November the 6th, ‘We can’t afford four more years,’” Romney said, with golfing great Jack Nicklaus, an Ohio native, at his side.

Romney pressed his economic message here after Ohio unemployment figures released last week showed marked improvement in some parts of the state. Ohio’s overall rate – 7.2 percent – is lower than the national average, and state jobless figures showed that it had dropped even more in some counties last month. In central Ohio, where Romney began Wednesday, the unemployment rate improved to 6.1 percent in August from 6.4 percent in July, the lowest rate in four years.

Even Republican Gov. John Kasich, who spoke at the Westerville rally before Romney, took note of the new numbers. “I hope you all know that Ohio’s coming back,” Kasich said. "From 48th in job creation to number 4 in the Midwest. . . . Our families are going back to work.”

Kasich notwithstanding, Romney argued that Ohio has gotten worse – not better – under Obama’s leadership, with lost jobs, an increase in the number of residents who receive food stamps and more people living in poverty. Romney also says the president hasn’t been tough enough on Chinese trade practices, which he argues has hurt the auto industry. Obama accused China last week of harming U.S. autoworkers by illegally subsidizing its own auto and auto parts industry, and he accused Romney of investing in China companies.

In Bowling Green, the president attributed the state’s improving economy in part to the auto industry bailout, which he supported and Romney opposed. One in every eight workers here is tied to the auto industry.

Obama also mocked Romney for a recent remark calling 47 percent of the country on government assistance “victims.”

“I don’t believe we can get very far with leaders who write off half the nation as a bunch of victims who never take responsibility for their own lives,’’ the president said.

William Blair, a retired city public-works director who attended the rally at Bowling Green State University, said the president’s policies were starting to resonate.

“I think Obama is getting his message out. Romney is falling on his face,” said Blair. He was standing next to his granddaughters, ages 8 and 6, wearing matching homemade red Obama T-shirts.

On the stump in Ohio and in television interviews Wednesday, Romney sought to show a more personal side. To address questions about his compassion, Romney pointed to something he rarely talks about: his Massachusetts health care law.

“I think throughout this campaign as well, we talked about my record in Massachusetts, don’t forget – I got everybody in my state insured,” Romney told NBC’s Ron Allen in Toledo. “One hundred percent of the kids in our state had health insurance. I don’t think there’s anything that shows more empathy and care about the people of this country than that kind of record.”

Romney senior adviser Kevin Madden denied that the candidate was struggling to get back into the game in Ohio.

“Our plan to campaign hard all across Ohio and Florida is based on our belief that this is a close race,’’ Madden said. “You don’t need a poll to tell you that voters are concerned about the direction of the economy under President Obama.’’

Obama campaign spokeswoman Jen Psaki said the election map appeared to be shifting toward the president and away from Romney. “The field is looking like it’s narrowing for them,” she said.